SOLUTION: the slope-intercept form of the equation of the line that passes through: (0,-4) and is perpendicular to {{{y = expr(3/2)x + 1}}}.

y = \large -\frac{3}{2} x + 1. 

That coding doesn't work on here.  But you meant this:



Comparing that to y = mx+b we see that the slope, m = 3/2.

A line perpendicular to it has the slope which is the
reciprocal of that slope with the sign changed.

So the slope of the desired line is  m = -2/3

We use the point-slope form, which is:





When we simplify the point-slope form, we will have the
slope-intercept form: 





Edwin